We consider the sample paths of the order statistics of independent and
identically distributed random variables with common distribution function
F. If F is strictly increasing but possibly having
discontinuities, we prove that the sample paths of the order statistics satisfy
the large deviation principle in the Skorokhod MM1 topology.
Sanov's theorem is deduced in the Skorokhod M'1 topology as a
corollary to this result. A number of illustrative examples are presented,
including applications to the sample paths of trimmed means and Hill plots.
Publié le : 2011-03-15
Classification:
Large deviation,
order statistic,
empirical law,
Skorokhod topology,
weak convergence,
60F10,
62G30
@article{1300198147,
author = {Duffy, Ken R. and Macci, Claudio and Torrisi, Giovanni Luca},
title = {Sample path large deviations for order statistics},
journal = {J. Appl. Probab.},
volume = {48},
number = {1},
year = {2011},
pages = { 238-257},
language = {en},
url = {http://dml.mathdoc.fr/item/1300198147}
}
Duffy, Ken R.; Macci, Claudio; Torrisi, Giovanni Luca. Sample path large deviations for order statistics. J. Appl. Probab., Tome 48 (2011) no. 1, pp. 238-257. http://gdmltest.u-ga.fr/item/1300198147/